Capital Asset Pricing Model with Size Factor and Normalizing by Volatility Index
Abstract
The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio. We insert size effect in CAPM, capturing the observation that small stocks have higher risk and return than large stocks, on average. Dividing stock index returns by the Volatility Index makes them independent and normal. In this article, we combine these ideas to create a new discrete-time model, which includes volatility, relative size, and CAPM. We fit this model using real-world data, prove the long-term stability, and connect this research to Stochastic Portfolio Theory. We fill important gaps in our previous article on CAPM with the size factor.
Keywords
Cite
@article{arxiv.2411.19444,
title = {Capital Asset Pricing Model with Size Factor and Normalizing by Volatility Index},
author = {Abraham Atsiwo and Andrey Sarantsev},
journal= {arXiv preprint arXiv:2411.19444},
year = {2026}
}
Comments
18 pages, 2 tables, 4 figures. Keywords: Capital Asset Pricing Model, stochastic volatility, ergodic Markov process, stationary distribution, size effect, autoregression, capital distribution curve